Disorder averaging and its UV discontents
Jonathan J. Heckman, Andrew P. Turner, Xingyang Yu
Abstract
We present a stringy realization of quantum field theory ensembles in $D\ensuremath{\le}4$ spacetime dimensions, thus realizing a disorder averaging over coupling constants. When each member of the ensemble is a conformal field theory with a standard semiclassical holographic dual of the same radius, the resulting bulk can be interpreted as a single asymptotically anti--de Sitter space geometry with a distribution of boundary components joined by wormhole configurations, as dictated by the Hartle--Hawking wave function. This provides a UV completion of a recent proposal by Marolf and Maxfield that there is a high-dimensional Hilbert space for baby universes, but one that is compatible with the proposed swampland constraints of McNamara and Vafa. This is possible because our construction is really an approximation that breaks down both at short distances, but also at low energies for objects with a large number of microstates. The construction thus provides an explicit set of counterexamples to various claims in the literature that holographic and effective field theory considerations can be reliably developed without reference to any UV completion.